Implicit (or semi-implicit) numerical schemes are useful numerical methods to solve advection dominated problems in several circumstances [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}, [15]}, [16]}. They can avoid or reduce significantly the main disadvantage of fully explicit schemes that are implemented on a fixed mesh with a finite stencil in numerical discretization. Such explicit schemes based on finite difference or finite volume methods require a stability restriction on the choice of discretization parameters [17]}, e.g. the time step. This can be disadvantageous in several situations like highly variable velocity field or nonuniform space discretization step [4]}, [19]} or long time simulations when approaching stationary solutions [14]}. Another important type of problems when implicit schemes can be useful are stiff differential equations involving the advection term [3]}, [22]}, [9]}, [11]}.
